Diode devices based on superconductivity

ABSTRACT

An electronic device (e.g., a diode) is provided that includes a substrate and a patterned layer of superconducting material disposed over the substrate. The patterned layer forms a first electrode, a second electrode, and a loop coupling the first electrode with the second electrode by a first channel and a second channel. The first channel and the second channel have different minimum widths. For a range of current magnitudes, when a magnetic field is applied to the patterned layer of superconducting material, the conductance from the first electrode to the second electrode is greater than the conductance from the second electrode to the first electrode.

RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.16/182,513, filed on Nov. 6, 2018, entitled “Diode Devices Based onSuperconductivity,” which claims priority to U.S. Provisional PatentApplication 62/582,789, filed on Nov. 7, 2017, entitled “Diode DevicesBased on Superconductivity,” each of which is hereby incorporated byreference in its entirety.

TECHNICAL FIELD

This relates generally to electronic devices (e.g., diodes) having anasymmetric conductance between terminals and, more specifically, todiodes that operate based on the properties of superconductingmaterials.

BACKGROUND

In electrical circuits, there is often a need for allowing electriccurrent to flow in one direction but not the other. Diodes provide thisfunctionality and are ubiquitous in modern electronics. A diode commonlyrefers to a two-terminal electronic component that conducts primarily inone direction (e.g., has an asymmetric conductance between the twoterminals, often referred to as electrodes). Over the years, diodes havetaken a variety of forms, from thermionic diodes (based on vacuum tubes)to semiconductor-based diodes using point contacts or n-p junctions.

However, conventional diodes, even in the high conductance direction,have non-zero resistances. Thus, applications of conventional diodeshave been limited.

SUMMARY

Accordingly, there are needs for diodes that have zero resistance in thehigh conductance direction. The present disclosure provides thin filmdiode devices based on superconducting materials, thereby utilizingadvantages of superconducting materials (e.g., zero resistance undercertain conditions). In addition, diodes that are superconducting can beintegrated more easily (e.g., monolithically) with other superconductingcomponents in circuits and devices. Such circuits and devices are oftenused for making sensitive measurements. For example, superconductingcircuits play a critical role in superconducting quantum interferencedevices (SQUIDs). Superconducting components also play an important rolein sensitive optical measurements. For these purposes, there is a needfor diodes whose operating principles are based on the properties ofsuperconducting materials.

In accordance with some embodiments, an electronic device (e.g., a diodedevice) is provided that includes a substrate and a patterned layer ofsuperconducting material disposed over the substrate. The patternedlayer forms a first electrode, a second electrode, and a loop couplingthe first electrode with the second electrode by a first channel and asecond channel. The first channel has a first minimum width and thesecond channel has a second minimum width that is distinct from thefirst minimum width. The electronic device further includes a magnetconfigured to apply a magnetic field to the loop in the patterned layerof superconducting material. The magnetic field produces an expulsioncurrent in the loop that travels toward the second electrode in thefirst channel and toward the first electrode in the second channel. Fora range of current magnitudes, when the magnetic field is applied to thepatterned layer of superconducting material, the conductance from thefirst electrode to the second electrode is greater than the conductancefrom the second electrode to the first electrode.

Additionally, the present disclosure provides a method of using a thinfilm diode device based on superconducting materials. The methodincludes obtaining an electrical device that includes a substrate and apatterned layer of superconducting material disposed over the substrate.The patterned layer forms a first electrode, a second electrode, and aloop coupling the first electrode with the second electrode by a firstchannel and a second channel. The first channel has a first minimumwidth and the second channel has a second minimum width that is distinctfrom the first minimum width. The method further includes applying amagnetic field over the loop in the patterned layer of superconductingmaterial. The method further includes, while the magnetic field isapplied over the loop: applying a first current from the first electrodeto the second electrode, whereby the superconducting material in theloop remains in a superconducting state; and applying the first currentfrom the second electrode to the first electrode, whereby thesuperconducting material in the loop transitions into anon-superconducting state.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the various described implementations,reference should be made to the Detailed Description below, inconjunction with the following drawings in which like reference numeralsrefer to corresponding parts throughout the figures.

FIG. 1A is a front view of a portion of an electronic device (e.g., asuperconducting diode device) in accordance with some embodiments.

FIG. 1B is a plan view of the portion of the electronic device shown inFIG. 1A.

FIG. 1C illustrates an equivalent circuit that corresponds to theportion of the electronic device shown in FIGS. 1A and 1B.

FIG. 2 illustrates a magnetic field applied to a portion of a patternedlayer of superconducting material of the electronic device in accordancewith some embodiments.

FIGS. 3A-3B illustrate magnets for applying a magnetic field to apatterned layer of superconducting material in accordance with someembodiments.

FIG. 4 illustrates the operation of a superconducting diode inaccordance with some embodiments.

FIG. 5 illustrates example geometries of superconducting loops having afirst channel and a second channel with different minimum widths inaccordance with some embodiments.

FIG. 6 illustrates a method using a diode device based onsuperconducting materials in accordance with some embodiments.

DETAILED DESCRIPTION

The diodes described herein operate based on particular properties ofsuperconducting materials, namely that superconducting materialsbecoming resistive (e.g., non-superconductive) under certain conditions.For example, a superconducting material superconducts (e.g., have zeroelectrical resistance) only below a particular temperature (called thematerial's critical temperature) (e.g., the superconducting material isin a superconducting state having zero electrical resistance only belowthe particular temperature). This temperature is specific to theparticular superconducting material and varies with the ambientpressure. For example, at one atmosphere of pressure (e.g., 101 kPa),niobium (Nb) superconducts below 9.26 kelvin while niobium oxide (NbO)superconducts below 1.38 kelvin. In addition, superconducting materialscan support only a limited density of electrical current beforetransitioning to a resistive state. The limit on the amount of currentdensity that the superconducting material can support before becomingresistive is called the critical current density. For example, asuperconducting material conducts a current having a current densitybelow the critical current density with no electrical resistance (e.g.,at a temperature below the superconducting material's criticaltemperature) and the superconducting material conducts a current havinga current density above the critical current density with non-zeroelectrical resistance (e.g., even at a temperature below thesuperconducting material's critical temperature). The critical currentdensity is also specific to the material and dependent on the ambientpressure.

Another property of superconductors is that a superconducting materialin a superconducting state expels an applied magnetic field. Forexample, when a magnetic field is applied over a loop (e.g., asuperconducting wire having a loop shape), a loop of current (calledexpulsion or screening current) is established in the superconductingmaterial in response to the applied magnetic field. The current loopcreates a magnetic field that is opposite the applied magnetic field andthe created magnetic field cancels out the applied magnetic field.

The devices described herein take advantage of these effects. Inparticular, the present disclosure provides a diode (e.g., a thin filmdiode) that operates based on superconductivity. The diode includes alayer of superconducting material deposited and patterned on asubstrate. The pattern forms two electrodes (e.g., wires ofsuperconducting material) and a loop of superconducting materialcoupling the two electrodes. A magnet applies a magnetic field to theloop, resulting in an expulsion current that circles the loop. Becauseof the loop structure, the expulsion current travels toward oneelectrode (e.g., the anode) on one side of the loop, and toward theother electrode (e.g., the cathode) on the other side of the loop. Whena current is applied between the two electrodes, the applied currentacts in conjunction with the expulsion current. That is, the appliedcurrent adds to the expulsion current in one channel and subtracts fromthe expulsion current in the other channel.

By making the loop asymmetric so that one side of the loop (e.g., onechannel) is thinner than the other (e.g., a first side of the loop has aminimum width that is greater than a minimum width of a second side ofthe loop), the device can have an asymmetric conductance (e.g., while amagnetic field is applied). While a magnetic field is applied over theloop, the current density in an asymmetric loop is high when the appliedcurrent travels in the same direction as the expulsion current in thenarrow channel (e.g., if the same magnitude current were applied in theopposite direction, it would add to the expulsion current in the widerchannel and the resulting current density would not be as high, becausethe width of the wider channel is greater than the width of the narrowchannel). Thus, for at least some magnitudes of applied current, whenthe current is applied in one direction, a current density in the narrowchannel exceeds the critical current density. When the current densityin the narrow channel exceeds the critical current density, the narrowchannel transitions to a resistive (non-superconducting) state. In someembodiments, when the narrow channel transitions to a resistive(non-superconducting) state, a redistribution of the current also causesthe current density in the wide channel to exceed the critical currentdensity, causing the wide channel to transition to a resistive state aswell. This is referred to herein as an avalanche effect. When the samecurrent magnitude is applied in the opposite direction, the currentdensity in the narrow channel does not exceed the critical currentdensity and the narrow channel remains in a superconducting state.Because the device transitions to a resistive state when a current isapplied in one direction (e.g., both channels transition to a resistivestate when a current is applied in one direction), but remainssuperconducting when the same current is applied in the oppositedirection (for at least certain current magnitudes), the electricalconductance from the first electrode to the second electrode is greaterthan the electrical conductance from the second electrode to the firstelectrode. Thus, the device has an asymmetric conductance between thefirst electrode and the second electrode.

Reference will now be made in detail to implementations, examples ofwhich are illustrated in the accompanying drawings. In the followingdetailed description, numerous specific details are set forth in orderto provide a thorough understanding of the various describedimplementations. However, it will be apparent to one of ordinary skillin the art that the various described implementations may be practicedwithout these specific details. In other instances, well-known methods,procedures, components, circuits, and networks have not been describedin detail so as not to unnecessarily obscure aspects of theimplementations.

FIGS. 1A-1B illustrate a front view and a plan view of a portion of anelectronic device 100, respectively, in accordance with someembodiments. For visual clarity, magnet 122 (shown in FIG. 1A anddiscussed below) is excluded from the top-down view shown in FIG. 1B.FIG. 1C illustrates a circuit equivalent of electronic device 100, inaccordance with some embodiments. In some embodiments, electronic device100 includes a diode 102 (e.g., a thin film diode) and an inductiveelement 104 (e.g., an inductor). In some embodiments, diode 102 is atwo-terminal electronic component that conducts primarily in onedirection (e.g., has an asymmetric conductance between the twoterminals, often referred to as a first electrode and a secondelectrode).

In some embodiments, inductive element 104 has a pre-selected, ordesigned-for, inductance (e.g., as opposed to merely having an inherentinductance, which is a natural property of circuit components, includingwires). For example, patterned layer of superconducting material 108 ispatterned such that the shape of the inductive element 104 (e.g., asquiggly shape) results in a desired inductance. As explained withreference to FIG. 4, in some cases, inductive element 104 assures thatthe current traveling through diode 102 does not change too quickly by,for example, getting re-directed through a low-impedance portion of acircuit coupled with diode 102.

In some embodiments, electronic device 100 is a portion of asuperconducting circuit (e.g., electronic device 100 is electricallycoupled with other components to form a circuit). For example,electronic device 100 may be incorporated (e.g., monolithicallyintegrated) into a larger electronic device or superconducting circuit.Thus, electronic device 100 may form a portion or a component of alarger electronic device or superconducting circuit.

As used herein, the term “superconducting circuit” means a circuit forwhich some aspect of the circuit's functionality relies on thesuperconducting properties of superconducting materials. In someembodiments, a superconducting circuit includes a superconductingmaterial.

As used herein, the term “superconducting material” means a materialthat exhibits superconducting behavior under certain conditions (e.g.,temperature, pressure, magnetic, and current density conditions). Whenthose conditions are met, the superconducting material is said to be ina superconducting state. For example, a superconducting material is amaterial that operates as a superconductor (e.g., operates with zeroelectrical resistance) when cooled below a particular temperature(called the critical temperature) and having less than a thresholdcurrent density flowing through it (called the critical currentdensity). Depending on the conditions, a superconducting material mayalso be in a resistive, or non-superconducting, state (e.g., a state inwhich the material has a non-zero electrical resistance). For example, asuperconducting material supplied with a current that exceeds thecritical current density for the superconducting material transitionsfrom a superconducting state having zero electrical resistance to anon-superconducting state having non-zero electrical resistance. Thus,as used herein, a superconducting material is one that is capable ofsuperconducting under the right conditions, but need not always besuperconducting.

Returning to FIGS. 1A-1C, device 100 includes a substrate 106 (e.g., asilicon substrate, a quartz substrate, or any other suitable substrate).In some embodiments, some or all of the remaining components of device100 are fabricated upon (e.g., monolithically integrated with) substrate106. For example, device 100 includes a patterned layer ofsuperconducting material 108 disposed over the substrate (e.g., directlyon substrate 106 or with one or more intervening layers betweensubstrate 106 and the layer of superconducting material 108). Thepatterned layer of superconducting material 108 can be formed bydepositing the layer of the superconducting material (e.g., niobium,niobium oxide, etc.) using a standard deposition technique (e.g.,magnetron sputtering) and then patterning the deposited layer ofsuperconducting material using optical or e-beam lithography techniques.

The patterned layer of superconducting material 108 forms a firstelectrode 110-a (e.g., an anode) and a second electrode 110-b (e.g., acathode). In some embodiments, first electrode 110-a and secondelectrode 110-b are superconducting wires having widths in the range oftens of nanometers or hundreds of nanometers. As used herein, a “wire”is a section of material configured for transferring electrical current.In some implementations, a wire includes a section of materialconditionally capable of transferring electrical current (e.g., a wiremade of a superconducting material that is capable of transferringelectrical current while the wire is maintained at a temperature below acritical temperature). Thus, in the context of an integrated circuit, awire can be a patterned strip of a deposited conductive layer (e.g., alayer that conducts at least under certain conditions).

The patterned layer of superconducting material 108 forms a loop 112coupling first electrode 110-a with second electrode 110-b by a firstchannel 114-a and a second channel 114-b. First channel 114-a has afirst minimum width (shown at location 116-a) and second channel 114-bhas a second minimum width (shown at location 116-b) that is distinctfrom the first minimum width (e.g., the first minimum width is greaterthan the second minimum width).

As used herein, a loop has any shape with two separate, connected,channels. The term loop is not meant to imply any particular shape(e.g., a loop is not limited to a circular loop). As discussed below,the loop can have a circular outer perimeter, an oblong outer perimeter,or a rectangular outer perimeter. In some embodiments, a loop has anyshape having two conductive channels surrounding an insulating centerregion (e.g., insulating center region 118). In some embodiments, aportion of the superconducting layer is removed from the insulatingcenter region. In some embodiments, the insulating center region isfilled with an insulating material (e.g., passive layer 120, which maycover the patterned layer of superconducting material 108 and fill inthe gaps).

In some embodiments, second channel 114-b is configured (e.g., using theselection criteria, described below) to transition from asuperconducting state to a resistive state upon application of a currentfrom second electrode 110-b to first electrode 110-a, (e.g., as long asthe current has a magnitude in a range of current magnitudes for whichthe device operates, as described below). In some embodiments, upon theapplication of the current from second electrode 110-b to firstelectrode 110-a, first channel 114-a is configured to transition to aresistive state in response to second channel 114-b transitioning to aresistive state (e.g., via a cascade effect, described below).

Electronic device 100 further includes a magnet 122 configured to applya magnetic field to loop 112 in a patterned layer of superconductingmaterial 108. In some embodiments, magnet 122 is a permanent magnet. Insome embodiments, magnet 122 is an electromagnet. In some embodiments,magnet 122 (whether an electromagnet or permanent magnet) is fabricatedon substrate 106 to form an integral part of diode 102 (e.g., magnet 122is integrated with diode 102 on substrate 106). As used herein, the term“fabricated on” is not meant to imply direct contact between substrate106 and magnet 122. Rather, the term “fabricated on” contemplates thepossibility of one or more intervening layers between substrate 106 andmagnet 122 (e.g., patterned layer of superconducting material 108 andpassive layer 120). The exact ordering of layers is not necessarilyimportant. For example, in some embodiments, a magnet is disposeddirectly on the substrate, followed by a passive (e.g., insulating)layer, followed by a patterned layer of superconducting material (e.g.,the layer structure of electronic device 100 can be inverted). Theoperation of magnet 122 is described in greater detail with reference toFIG. 2.

FIG. 2 illustrates magnetic field 202 applied to a portion of thepatterned layer of superconducting material 108, in accordance with someembodiments (e.g., applied by magnet 122, FIG. 1A). In FIG. 2, magneticfield 202 represents a magnetic field that is directed into the page.Alternatively, a magnetic field that is directed out of the page may beused. As a result of the Meissner effect, when loop 112 is in asuperconducting state, application of magnetic field 202 results inexpulsion current I_(E) 204 (sometimes called a screening current)around loop 112 which expels magnetic field 202 from the superconductingmaterial. Because the expulsion current travels around loop 112 (e.g.,clockwise or counter-clockwise, depending on the direction of appliedmagnetic field 202), expulsion current I_(E) 204 travels from firstelectrode 110-a toward second electrode 110-b in first channel 114-a andfrom second electrode 110-b toward first electrode 110-a in secondchannel 114-b. In some embodiments, expulsion current I_(E) 204 travelstoward the anode (e.g., first electrode 110-a) in the narrow channel(e.g., channel 114-b), thus reducing the current density in the narrowchannel when a current is applied from the anode to the cathode (e.g.,second electrode 110-b), and increasing the current density in thenarrow channel when a current is applied from the cathode to the anode(triggering the transition to a resistive state).

FIGS. 3A-3B illustrate magnets for applying a magnetic field to apatterned layer of superconducting material, in accordance with someembodiments. For example, magnet 122 (FIG. 1A) can be embodied as eithermagnet 304 (FIG. 3A) or magnet 314 (FIG. 3B).

Magnet 304 is an electromagnet, in accordance with some embodiments. Asnoted above, in some embodiments, magnet 304 is integrated on asubstrate (e.g., substrate 106, FIG. 1A) with other diode components(e.g., patterned layer of superconducting material 108, FIGS. 1A-1B). Inother embodiments, magnet 304 is separate from substrate 106. In someembodiments, electromagnet 304 includes one or more coils of wire 306(or another wire structure designed to produce a current-based magneticfield). In some embodiments, electromagnet 304 includes magnetic core310 to enhance the strength of the magnetic field from electromagnet304. Electromagnet 304 further includes circuitry 308 that providescurrent to the one or more coils of wire 306 (e.g., current source 312and circuitry to control current source 312). In some embodiments, theone or more coils of wire 306 are integrated on substrate 106 butcircuitry 308 is separate from substrate 106.

In some embodiments, electromagnet 304 is configured to apply a tunablemagnetic field (e.g., by tuning the magnitude of the current throughcoils of wire 306) to the patterned layer of superconducting material108. This has the effect of tuning a range of current magnitudes forwhich the device operates as a diode (e.g., the range of currentmagnitudes for which the conductance from first electrode 110-a tosecond electrode 110-b is greater than the conductance from secondelectrode 110-b to the first electrode 110-a, or, more simply put, therange of current magnitudes for which the conductance is greater in onedirection than the other). To this end, in some embodiments, currentsource 312 is a tunable current source and circuitry 308 includescircuitry to control the tunable current source 312.

In accordance with some embodiments, magnet 314 (illustrated in FIG. 3B)is a permanent magnet. In some embodiments, permanent magnet 314 isintegrated on substrate 106. To that end, in some embodiments, magnet314 includes one or more magnetic layers 316 deposited on (e.g.,disposed over) substrate 106 (e.g., directly on substrate 106 or withone or more intervening layers between substrate 106 and the one or moremagnetic layers 316). The one or more magnetic layers 316 are optionallypatterned. In some embodiments, the one or more magnetic layers 316collectively exhibit a perpendicular magnetic anisotropy (e.g., magnet314 is a thin film magnet with perpendicular magnetic anisotropy). Insuch embodiments, magnetic field lines 318 emanate perpendicularly frommagnet 314 and are incident perpendicularly, or substantially so, onloop 112 (FIGS. 1A-1B). For example, some nickel/cobalt andpalladium/cobalt multilayer films exhibit perpendicular magneticanisotropy. In some embodiments, magnetic field lines 318 have acomponent perpendicular to loop 112 (e.g., magnet 314 is has an in-planeanisotropy and is positioned with respect to loop 112 to provide fieldlines with a perpendicular component to a plane defined by loop 112).

FIG. 4 illustrates the operation of a thin film superconducting diodethrough a series of frames 400, in accordance with some embodiments. Inconjunction with FIG. 4, the description below provides selectioncriteria from which loop 112 can be designed (e.g., to produce acascading or “avalanche” transition to a resistive state when a reversebias current is applied). In accordance with some embodiments, theselection criteria described below use simplifying assumptions, such asthat an applied current is initially distributed equally between channel114-a and channel 114-b. The current distributions can, however, inaccordance with some embodiments, be more accurately determined usingany of a variety of simulation tools, thus resulting in more accuratedesign of loop 112. The term “selection criteria” should therefore beconstrued as numerically or analytically calculated design constraintson the geometry of loop 112 (e.g., taking into account one or more of:the strength of the magnetic field from magnet 122, the critical currentdensity of the superconducting material, the critical temperature of thesuperconducting material, and a designed range of current magnitudes, asdescribed below). In some embodiments, the selection criteria provide aset of suitable values for the thickness of the superconducting materialas well as the minimum widths of first channel 114-a and second channel114-b, respectively, given an applied magnetic field and the propertiesof the superconducting material (e.g., critical current density andcritical temperature). The term “selection rule” is used below to denoteanalytical selection criteria (e.g., equations rather than numericalsimulations) based on simplifying assumptions (e.g., toy physical modelsof electronic device 100).

The selection criteria are governed by a range of current magnitudes forwhich the device should function as a diode. The range of currentmagnitudes can be denoted (I_(min), I_(max)). Thus, I_(min) is a lowerthreshold current for which the device ceases to exhibit an asymmetricconductance (e.g., the threshold bias current needed to cause loop 112to transition to a resistive state in reverse bias) and I_(max) is aupper threshold current for which the device ceases to exhibit anasymmetric conductance (e.g., the threshold current that causes loop 112to transition to a resistive state in forward bias). While a currentgreater than I_(max) is applied to the device in either direction, thedevice operates in a resistive state (e.g., when a current greater thanI_(max) is applied to the device in forward bias, the device operates ina resistive state; and when a current greater than I_(max) is applied tothe device in reverse bias, the device also operates in a resistivestate). While a current less than I_(min) is applied to the device ineither direction, the device operates in a superconducting state (e.g.,when a current less than I_(min) is applied to the device in forwardbias, the device operates in a superconducting state; and when a currentless than I_(min) is applied to the device in reverse bias, the devicealso operates in a superconducting state). While a current betweenI_(min) and I_(max) is applied in forward bias, the device operates in asuperconducting state; and while a current between I_(min) and I_(max)is applied in reverse bias, the device operates in a resistive state,thereby providing asymmetric conductance.

In some embodiments, I_(min) is the threshold reverse bias current,which causes second channel 114-b to transition to a resistive state. Insome embodiments, I_(max) is the threshold reverse bias current, whichcauses both first channel 114-a and second channel 114-b to transitionto a resistive state. In some embodiments, Lax is the threshold forwardbias current, which causes both channels (channel 114-a and channel114-b) to transition to a resistive state (concurrently orsequentially).

To that end, frame 400-1 illustrates loop 112 with applied current inforward bias. In forward bias, current 402 is applied from firstelectrode 110-a to second electrode 110-b. While current 402 is appliedfrom first electrode 110-a to the second electrode 110-b, a portion ofcurrent 402 is distributed through first channel 114-a (the portiondistributed through first channel 114-a is labeled current 402-a) and aportion of current 402 is initially distributed through second channel114-b (the portion distributed through second channel 114-b is labeledcurrent 402-b). In some embodiments, current 402 is at least initiallydistributed equally between channel 114-a and channel 114-b, resultingin current 402-a and current 402-b being equal.

When forward bias current 402 has a magnitude in the range of currentmagnitudes (I_(min), I_(max)), loop 112 remains in a superconductingstate. To that end, first channel 114-a is configured (e.g., via theselection criteria) so that, when the current is applied from firstelectrode 110-a to second electrode 110-b (e.g., in forward bias), theportion of the current initially distributed through first channel 114-a(i.e., current 402-a), added to the expulsion current I_(E) in firstchannel 114-a, results in a current density in first channel 114-a thatremains below a critical current density of the superconductingmaterial. Further, the portion of the current initially distributedthrough second channel 114-b (i.e., current 402-b), reduced by theexpulsion current I_(E) in second channel 114-b, results in a currentdensity in second channel 114-b that remains below a critical currentdensity of the superconducting material. By definition, these criteriaremain valid for the maximum current in the range of current magnitudes.To that end, the maximum current I_(max) in the range of currentmagnitudes gives rise to the following selection rules:

$\begin{matrix}{{\frac{I_{E} + {0.5 \times I_{{ma}\; x}}}{A_{1}} = {\frac{I_{E} + {0.5 \times I_{m\;{ax}}}}{w_{1} \times t} < j_{c}}};} & (1) \\{{\frac{I_{E} - {0.5 \times I_{{ma}\; x}}}{A_{2}} = {\frac{I_{E} - {0.5 \times I_{{ma}\; x}}}{w_{2} \times t} < j_{c}}};} & (2)\end{matrix}$where I_(E) is the expulsion current (which varies with the appliedmagnetic field), A₁ is the cross-sectional area of the narrowest part(e.g., a part having a smallest cross-sectional area) of first channel114-a, and A₂ is the cross-sectional area of the narrowest part (e.g., apart having a smallest cross-sectional area) of second channel 114-b.When the first channel and the second channel have a same thickness t ofthe layer of superconducting material (e.g., layer 108, FIG. 1A), w₁ isthe first minimum width (e.g., the minimum width of first channel114-a), and w₂ is the second minimum width (e.g., the minimum width ofthe second channel 114-b, which is less than the first minimum width).In some embodiments, the thickness of the layer of superconductingmaterial varies between first channel 114-a and second channel 114-b,but a uniform thickness simplifies the process of manufacturing loop112.

Frames 400-2 through 400-4 illustrate loop 112 in reverse bias, in whichapplication of current 404 from second electrode 110-b to firstelectrode 110-a results in loop 112 transitioning to a resistive state(e.g., a non-superconducting state).

Frame 400-2 illustrates the moment current 404 greater than or equal toI_(min) is applied to loop 112 in reverse bias. Initially, a portion ofcurrent 404 is distributed through first channel 114-a (the portiondistributed through first channel 114-a is labeled current 404-a) and aportion of current 404 is distributed through second channel 114-b (theportion distributed through second channel 114-b is labeled current404-b). In some embodiments, current 404 initially distributes equallybetween channel 114-a and channel 114-b, resulting in current 404-a andcurrent 404-b being equal. Second channel 114-b is configured (e.g., bychoice of shape and size, according the selection criteria) so that,when current 404 is applied (in reverse bias) from second electrode110-b to first electrode 110-a, the portion of the current initiallydistributed through second channel 114-b (i.e., current 404-b), added tothe expulsion current in second channel 114-b, results in a currentdensity in second channel 114-b that exceeds a critical current densityof the superconducting material. Because current 404 is above theminimum current I_(min) in the range of current magnitudes, appliedcurrent 404 causes second channel 114-b (i.e., the narrower channel) totransition to a resistive state, as illustrated by resistive region 406of channel 114-b as shown in frame 400-3. This requirement that secondchannel 114-b become resistive for a reverse bias current within therange of current magnitudes gives rise to the following selection rule.

$\begin{matrix}{\frac{I_{E} + {0.5 \times I_{\min}}}{A_{2}} = {\frac{I_{E} + {0.5 \times I_{\min}}}{w_{2} \times t} > {j_{c}.}}} & (3)\end{matrix}$

With channel 114-a in a superconducting state and channel 114-b in aresistive state, regardless of the channel 114-b's resistance, all ornearly all of the current 404 is redistributed. In addition, becausechannel 114-b of loop 112 is no longer superconducting (e.g., loop 112has a resistive portion, namely channel 114-b), loop 112 no longersupports expulsion current I_(E) (e.g., the expulsion current isdissipated as heat in resistive region 406).

When current 404 is redistributed to the remaining superconductingchannel 114-a as shown in frame 400-3, current 404 causes an increase inthe current density in channel 114-a. This continues the avalancheeffect of switching loop 112 to a resistive state. To ensure that all ornearly all of current 404 is redistributed through the remainingsuperconducting channel 114-a (instead of redistributing through aportion of a larger circuit coupled with device 100, which may have alow impedance and thus tend to sink current), device 100 includesinductor 104 shown in FIG. 1. Inductor 104 (FIG. 1) is in series withloop 112 and thus limits the rate of change of the total currenttraveling from electrode 110-a to electrode 110-b (e.g., prevents adiscontinuous change in the total current traveling from electrode 110-ato 110-b). In some embodiments, inductor 104 is coupled with electrode110-a. In some embodiments, inductor 104 is coupled with electrode110-b. In some embodiments, a first inductor is coupled with electrode110-a and a second inductor that is distinct and separate from the firstinductor is coupled with electrode 110-b.

The increased current density in channel 114-a (caused by theredistribution of current 404 from channel 114-b to channel 114-a)exceeds the critical current density. The result is an avalanche effectwhereby channel 114-a transitions to a resistive state in response tochannel 114-b transitioning to a resistive state (as illustrated byresistive region 408 in channel 114-a, frame 400-4). Thus, applicationof a reverse bias current within the range of current magnitudes causesthe entire path between electrode 110-b and electrode 110-a to becomeresistive, resulting in the conductance asymmetry that gives rise to thedevice's operation as a diode. The cascade effect thus gives rise to thefinal selection rule:

$\begin{matrix}{\frac{I_{m\; i\; n}}{A_{1}} = {\frac{I_{m\; i\; n}}{w_{1} \times t} > {j_{c}.}}} & (4)\end{matrix}$

Frame 400-4 occurs a short time after frame 400-3. Frame 400-4illustrates the final effect of the current on the state of loop 112,namely that both channel 114-a and channel 114-b have become resistive.In some embodiments, the resistive portion of channel 114-b is largerthan it was in frame 400-3, which results from the residual currents inchannel 114-b creating heat (because channel 114-b is now resistive) andraising an expanded portion of channel 114-b above the criticaltemperature.

In some circumstances, the selection rules are written as:

$\begin{matrix}{{{I_{0} - I_{E}} < I_{C} \leq {I_{0} + I_{E}}};} & (5) \\{{{I_{0} + I_{E}} < {\frac{w_{1}}{w_{2}}I_{C}} \leq {2 \times I_{0}}};} & (6) \\{{I_{E} < I_{C}};} & (7) \\{w_{1} > {w_{2}.}} & (8)\end{matrix}$In Equations (5)-(8), I₀ is the current through each channel 114 andI_(C) is the critical current for the narrow channel (e.g., channel114-b). The range of applied currents 2×I₀ under which Equations (5)-(8)hold true, given the device's geometry and specifications, provides therange of currents (I_(min), I_(max)) in Equations (1)-(4). The left-handinequalities in Equations (5)-(6) provide conditions for which thedevice remains superconducting under forward bias. The right-handinequalities in Equations (5)-(6) provide conditions under which thedevice transitions to a resistive state in reverse bias. Equation (7)provides a maximum expulsion current, above which the expulsion currentquenches the loop and causes it to become resistive even in the absenceof an applied current. Equation (8) states that channel 114-a is thewider channel (vis-à-vis channel 114-b).

FIG. 5 illustrates example geometries of superconducting loops 500having a first channel and a second channel with differing minimumwidths (e.g., the first channel has a first minimum width and the secondchannel has a second minimum width that is distinct from the firstminimum width) in accordance with some embodiments. In accordance withsome embodiments, each of loop 500-1 and loop 500-2 has a shapecomprising an outer ellipse (e.g., circle) and an inner ellipse (e.g.,circle) that is eccentric to the outer ellipse resulting in a firstminimum width of the first channel and a second minimum width, distinctfrom the first minimum width, of the second channel. Thus, theeccentricity between the outer ellipse and the inner ellipse results inthe different minimum widths of the first channel and the secondchannel. As used herein, the term ellipse includes an oval.

In accordance with some embodiments, as shown in loop 500-3 and loop500-4, the second channel has a notch formed therein resulting in thesecond minimum width being less than the first minimum width (e.g., thepatterned layer of superconducting material is patterned such that anotch of insulating material extends into the second channel,constricting the conductive path of the second channel and defining aminimum width of the second channel that is less than a minimum width ofthe first channel). In some embodiments, loop 500-4 is shaped by twoconcentric circles, where one side of the other circled has such a notchformed therein. In some embodiments, rather than ellipses, the firstchannel and the second channel are formed by rectangles (or any othershape). The rectangles can be off-center relative to one another (e.g.,in an analogous fashion to the ellipses shown in loop 500-1 and loop500-2), or one rectangle can include a constricting notch (e.g., in ananalogous fashion to the constricting notches shown in loop 500-3 andloop 500-4), or both. In some embodiments, a first notch is defined inthe first channel and a second notch is defined in the second channel sothat a first minimum width of the first channel defined by the firstnotch is greater than a second minimum width of the second channeldefined by the second notch. One of skill in the art will recognizenumerous ways to pattern a layer of superconducting material so as tocreate two channels whereby the two channels have differing minimumwidths.

FIG. 6 illustrates method 600 of using an electrical device (e.g., diodedevice) based on superconducting materials, in accordance with someembodiments. The method includes obtaining (602) an electrical devicethat includes a substrate (e.g., substrate 106, FIG. 1A) and a patternedlayer of superconducting material disposed over the substrate (e.g.,patterned superconductor 108, FIGS. 1A-1B). The patterned layer forms afirst electrode (e.g., electrode 110-a, FIG. 1B), a second electrode(e.g., electrode 110-b, FIG. 1B), and a loop coupling the firstelectrode with the second electrode by a first channel and a secondchannel (e.g., loop 112 couples electrode 110-a and electrode 110-b bychannel 114-a and channel 114-b, FIG. 1B). The first channel has a firstminimum width and the second channel has a second minimum width that isdistinct from the first minimum width (e.g., as shown in FIGS. 1B, 2, 4,and 5). In some embodiments, the electronic device has any of thefeatures described with reference to FIGS. 1A-1C through FIG. 5.

In some embodiments, method 600 includes cooling (604) (e.g.,cryogenically) the electronic device below a critical temperature of thesuperconducting material. In some embodiments, the cooling is performedusing any cooling technology that can reach the critical temperature ofthe superconducting material. For high-temperature superconductors,these technologies include cooling with liquid nitrogen. Forlower-temperature superconductors, technologies such as dilutionrefrigeration, adiabatic demagnetization, and helium refrigeration canbe used.

Method 600 includes applying (606) a magnetic field over the loop in thepatterned layer of superconducting material. In some embodiments, themagnetic field has a predefined magnitude at the surface of thepatterned layer of superconducting material. In some embodiments, themagnetic field is applied substantially perpendicularly to the patternedlayer of superconducting material. In some embodiments, the magneticfield is applied using a magnet that is integrated with the electronicdevice (e.g., as shown in FIG. 1A and described with reference to FIGS.3A-3B). In some embodiments, the magnetic field is applied using anexternal magnet.

Method 600 includes, while the magnetic field is applied over the loop:applying (608) a first current from the first electrode to the secondelectrode, whereby the superconducting material in the loop remains in asuperconducting state, and applying the first current from the secondelectrode to the first electrode, whereby the superconducting materialin the loop transitions into a non-superconducting state.

In some embodiments, method 600 includes tuning the magnetic field(e.g., tuning the magnitude of the magnetic field) to tune a range ofcurrent magnitudes for which the loop exhibits asymmetric conductancewhereby the superconducting material in the loop remains in asuperconducting state when the first current is applied from the firstelectrode to the second electrode and whereby the superconductingmaterial in the loop transitions into a non-superconducting state whenthe first current is applied from the second electrode to the firstelectrode.

The terminology used in the description of the various describedimplementations herein is for the purpose of describing particularimplementations only and is not intended to be limiting. As used in thedescription of the various described implementations and the appendedclaims, the singular forms “a”, “an” and “the” are intended to includethe plural forms as well, unless the context clearly indicatesotherwise. It will also be understood that the term “and/or” as usedherein refers to and encompasses any and all possible combinations ofone or more of the associated listed items. It will be furtherunderstood that the terms “includes,” “including,” “comprises,” and/or“comprising,” when used in this specification, specify the presence ofstated features, integers, steps, operations, elements, and/orcomponents, but do not preclude the presence or addition of one or moreother features, integers, steps, operations, elements, components,and/or groups thereof.

It will also be understood that, although the terms first, second, etc.are, in some instances, used herein to describe various elements, theseelements should not be limited by these terms. These terms are only usedto distinguish one element from another. For example, a first currentcould be termed a second current, and, similarly, a second current couldbe termed a first current, without departing from the scope of thevarious described implementations. The first current and the secondcurrent are both currents, but they are not the same current unlessexplicitly stated as such.

As used herein, the term “if” is, optionally, construed to mean “when”or “upon” or “in response to determining” or “in response to detecting”or “in accordance with a determination that,” depending on the context.

The foregoing description, for purpose of explanation, has beendescribed with reference to specific implementations. However, theillustrative discussions above are not intended to be exhaustive or tolimit the scope of the claims to the precise forms disclosed. Manymodifications and variations are possible in view of the aboveteachings. The implementations were chosen in order to best explain theprinciples underlying the claims and their practical applications, tothereby enable others skilled in the art to best use the implementationswith various modifications as are suited to the particular usescontemplated.

What is claimed is:
 1. An electronic device, comprising: a substrate; apatterned layer of superconducting material disposed over the substrate,the patterned layer forming: a first electrode; a second electrode; anda loop coupling the first electrode with the second electrode by a firstchannel and a second channel, wherein the first channel has a firstminimum width and the second channel has a second minimum width that isdistinct from the first minimum width; wherein, for a range of currentmagnitudes, when a magnetic field is applied to the patterned layer ofsuperconducting material, the conductance from the first electrode tothe second electrode is greater than the conductance from the secondelectrode to the first electrode.
 2. The electronic device of claim 1,further comprising a magnet configured to apply the magnetic field tothe loop in the patterned layer of superconducting material, wherein themagnetic field produces an expulsion current in the loop.
 3. Theelectronic device of claim 2, wherein the magnet is an electromagnet. 4.The electronic device of claim 3, wherein the electromagnet isfabricated on the substrate to form an integral part of the electronicdevice, the electromagnet comprising: one or more coils of wire; andcircuitry to provide current to the one or more coils of wire.
 5. Theelectronic device of claim 3, wherein the electromagnet is configured toapply a tunable magnetic field to the patterned layer of superconductingmaterial to tune the range of current magnitudes for which theconductance from the first electrode to the second electrode is greaterthan the conductance from the second electrode to the first electrode.6. The electronic device of claim 2, wherein the magnet is a permanentmagnet.
 7. The electronic device of claim 6, wherein the permanentmagnet comprises one or more magnetic layers disposed over thesubstrate, the one or more magnetic layers collectively having aperpendicular magnetic anisotropy.
 8. The electronic device of claim 2,wherein the magnet is integrated with the electronic device on thesubstrate.
 9. The electronic device of claim 2, wherein: the firstminimum width is greater than the second minimum width; and the secondchannel is configured to transition to a resistive state uponapplication of a current from the second electrode to the firstelectrode having a magnitude in the range of current magnitudes.
 10. Theelectronic device of claim 9, wherein: upon the application of thecurrent from the second electrode to the first electrode, the firstchannel is configured to transition to a resistive state in response tothe second channel transitioning to a resistive state.
 11. Theelectronic device of claim 9, wherein: the expulsion current travelstoward the first electrode in the second channel; when the current isapplied from the second electrode to the first electrode, a portion ofthe current is initially distributed through the second channel; and thesecond channel is configured so that, when the current is applied fromthe second electrode to the first electrode, the portion of the currentinitially distributed through the second channel, added to the expulsioncurrent in the second channel, results in a current density in thesecond channel that exceeds a critical current density of thesuperconducting material.
 12. The electronic device of claim 11,wherein: the second channel is configured so that, when the current isapplied from the first electrode to the second electrode, the portion ofthe current initially distributed through the second channel, reduced bythe expulsion current in the second channel, results in a currentdensity in the second channel that remains below a critical currentdensity of the superconducting material.
 13. The electronic device ofclaim 1, wherein the loop has a shape comprising an outer ellipse and aninner ellipse that is eccentric to the outer ellipse resulting in thefirst minimum width and the distinct second minimum width of the firstchannel and the second channel, respectively.
 14. The electronic deviceof claim 1, wherein the second channel has a notch formed thereinresulting in the first minimum width being less than the second minimumwidth.
 15. The electronic device of claim 1, further comprising aninductive element.
 16. The electronic device of claim 1, wherein theelectronic device is a two-terminal device.